This preprint develops the axiomatic and ontological framework underlying the concept of quasi-magnitude and coherent collapse. It formalizes a pre-collapsed domain of quasi-states from which classical real numbers emerge as highly restricted projections. The article provides the formal mechanism that complements earlier structural and geometric analyses of the real line, clarifying how sign, order, absolute value, and commutativity arise as emergent consequences of collapse rather than as primitive properties. This work is intended to serve as the logical core of a broader program on quasi-numerical structures and their extensions beyond the real line. This work forms part of the research program Model of General Quasi-Coherence (MGQC).
This preprint develops the axiomatic and ontological framework underlying the concept of quasi-magnitude and coherent collapse. It formalizes a pre-collapsed domain of quasi-states from which classical real numbers emerge as highly restricted projections. The article provides the formal mechanism that complements earlier structural and geometric analyses of the real line, clarifying how sign, order, absolute value, and commutativity arise as emergent consequences of collapse rather than as primitive properties. This work is intended to serve as the logical core of a broader program on quasi-numerical structures and their extensions beyond the real line. This work forms part of the research program Model of General Quasi-Coherence (MGQC).
This preprint develops a structural reinterpretation of quantum collapse within the Model of General Quasi-Coherence (MGQC). The article does not claim to replace standard quantum mechanics or to provide a completed physical theory. Its aim is more limited and foundational: to propose a mathematical and conceptual framework in which part of the apparent indeterminacy of measurement may be reconsidered as an effect of structural projection under a severely restricted observational regime. The paper introduces the quasi-number Q=(r,θ,τ,μ) as a structured state of magnitude, orientation, torsion, and structural accumulation, and studies a non-injective collapse map from a richer state domain to scalar visible output. On this basis, the article examines collapse multiplicity, apparent randomness, phase suppression, noncommutativity as structurally accumulated order-dependence, and a cautious fibered interpretation of the collapse architecture. It also discusses the distinction between geometric rank and internal structural richness in D1-, D2-, and D3-type regimes. The contribution of the preprint is foundational and structural rather than fully predictive. It is intended as a work in mathematical foundations and theoretical interpretation, and as part of an ongoing research program aimed at clarifying the relation between structured antecedent states, collapse, and visible measurement output. This preprint forms part of the Model of General Quasi-Coherence (MGQC) research program. The author publishes under the name Antonio Dominguez-Digat. Earlier records may appear under Antonio Domínguez, Antonio Dominguez, or Antonio Dominguez Digat.
Abstract This work presents a structural ontology of quantum mechanics grounded in the limits of formal description, rather than in interpretative models. Instead of proposing a new interpretation, modification of equations, or metaphysical extension, the text identifies a missing structural layer implicitly assumed by quantum theory: the necessity of filtration in systems operating beyond formal completeness. Drawing on Gödel’s incompleteness theorems as a structural precedent, the analysis reframes core quantum phenomena — superposition, collapse, entanglement, uncertainty, and wave–particle duality — as expressions of constrained potential rather than paradoxical physical behavior. Quantum mechanics is shown to operate in a pre-physical regime, describing admissible possibilities prior to enforced resolution, while classical physics describes the outcome of irreversible constraint. From this perspective, collapse is not caused by observation, randomness, or consciousness, but by saturation of coherence under applied constraints. Uncertainty emerges as a logical consequence of non-coexistent descriptions within a single formal frame, rather than as an epistemic limitation. The work then generalizes this framework beyond physics, demonstrating that entropy, irreversibility, and systemic collapse arise when systems continue operating beyond their Gödelian limits without a heuristic capable of recognizing formal exhaustion. This leads to a distinction between reintegrative (pre-Gödel) entropy and residual (post-Gödel) entropy regimes, with implications for computation, cognition, artificial systems, and large-scale systemic viability. This document is descriptive, not prescriptive.It introduces no implementations and proposes no cosmological mechanisms.Its contribution is the explicit articulation of structural constraints that any coherent physical or systemic description must satisfy.
The quasi-classical world of modern physics is a class of classical worlds superposed, literally a 'metaworld'. The measurement problem is itself evidence for the two different types of world, at the different levels of logical type. The enactment of linear dynamics in the classical worlds alters the class invariant, and thus induces physical collapse of the metaworld to a subclass. The complex formalism that seems deeply counterintuitive is class arithmetic. Measurement: set-selection of a subclass compatible with the observed outcome. Observable operators: partition of the class. Projection operators: set-selection of a subclass. Fourier transforms: switching set-selection. The uncertainty principle: incompatible set-selections. All the familiar structures of the formalism are transformed from postulates to inherent attributes of the class structure. The Born rule, unitary evolution, the complex structure of amplitudes, the probabilistic character of prediction, and the wave-mechanical form of the theory emerge as outputs of the ontology rather than independent axioms. The wavefunction is real. It is the ontological architecture of the metaworld and the reality of the quasi-classical world. The classical world, quantum mechanics and relativistic physics are unified in logical types.
We develop a pre-geometric reconstruction framework in which quantum mechanics, entanglement structure, gauge symmetry, locality, Lorentzian spacetime geometry, gravitation, and physical constants emerge from recursively stabilized coherent Hilbert-relational organization. The framework begins from a primitive coherent substrate consisting of compositional accessibility relations and complex transport amplitudes. No background spacetime manifold, metric geometry, or particle ontology is assumed fundamentally. The central proposal is that coherent Hilbert structure is more fundamental than spacetime geometry. Observable spacetime emerges through projection stabilization: a physical stability-selection mechanism dynamically selecting recursively stable coherent sectors from deeper relational structure. Quantum mechanics emerges from norm-preserving coherent transport. Entanglement emerges from nonfactorizable relational closure. Gauge symmetry emerges as redundancy of coherent transport representation. Classicality emerges through decoherence and stability selection. Lorentzian geometry emerges statistically from projected accessibility organization. Gravitation emerges thermodynamically as equilibrium relaxation of projected geometry. The framework is presented not as a completed unified theory, but as a reconstruction program aimed at explaining why physical reality organizes itself through Hilbert structure, gauge redundancy, locality, spacetime geometry, and thermodynamic gravitational dynamics.
Collapse-Induced Time Asymmetry and the Emergence of Classical Reality proposes a collapse-driven framework in which the emergence of classical definiteness and the arrow of time arise from the same underlying physical mechanism. Wavefunction collapse is treated as an intrinsic, irreversible process that progressively restricts the space of admissible quantum states, generating both temporal order and classical structure without reliance on observers, special boundary conditions, or externally imposed time asymmetry. The central contribution of this work is the introduction of an emergent collapse-ordering parameter, distinct from coordinate time, which indexes irreversible collapse events and provides a microscopic foundation for temporal asymmetry. Within this framework, stochastic localization resolves quantum indeterminacy, stabilizes macroscopic outcomes, and yields definite mass–energy configurations from which classical spacetime structure can emerge. Gravitational self-energy is reinterpreted not as the cause of collapse, but as a diagnostic of the energetic incompatibility between unrealized quantum alternatives. Collapse dynamics, entropy production, and geometric structure are shown to be mutually consistent aspects of a single irreversible process. The resulting picture unifies measurement resolution, the arrow of time, and classical emergence within a single collapse-based dynamical framework. This paper focuses on the theoretical structure and internal consistency of the proposed mechanism. A separate, accompanying repository paper will present proof-of-principle numerical simulations exploring collapse-driven information pruning, history-dependent backreaction, and emergent geometric behavior. These simulations are intended to illustrate qualitative features of the framework and to demonstrate dynamical stability and repeatability, rather than to provide quantitative gravitational modeling. Together, the theoretical analysis and forthcoming simulation results aim to clarify the physical role of collapse in the emergence of classical reality and temporal order.A companion repository containing proof-of-principle numerical simulations is available at Zenodo 10.5281/zenodo.18828923
The mathematical representation of the universe consists of sequences of symbols, rules and operators containing Gödel's undecidable propositions: information and its manipulation, also with Turing Machines. Classical information theory and mathematics, ideally independent from the medium used, can be interpreted realistically and objectively from their correspondence with quantum information, which is physical. Each representation of the universe and its evolution are, in any case, physical subsets of the universe, structured sets of observers and their complements in the universe made with spacetime events generated by local quantum measurements. Their description becomes a semantically closed structure without a global object-environment loss of decoherence as a von Neumann's universal constructor with a semantical abstract whose structure cannot be decided deterministically a priori from an internal observer. In a semantically closed structure, the realization of a specific event that writes the semantical abstract of the constructor is a problem of finding "which way" for the evolution of the universe as a choice of the constructor's state in a metastructure, like the many-world Everett scenario, from a specific result of any quantum measurement, corresponding to a Gödel undecidable proposition for an internal observer.